Hashtables use a lot of memory but can be very fast searches, in linear time.

In general you should use the data structure that best fits what you want to do, rather than trying to find the most efficient way.

``` [TODO:]
Use asymptotic behaviour to decide, most importantly seeing how the
structure will be used: an infrequent operation does not need to be
fast if it means everything else will be much faster
```

``` [TODO:]
Can use a table like this one to compare the asymptotic behaviour of every
structure for every operation on it.
```

Sequences (aka lists):

 Dynamic Array Array Deque Singly Linked List Double Linked List Push (Front) O(n) O(1) O(1) O(1) Pop (Front) O(n) O(1) O(1) O(1) Push (Back) O(1) O(1) O(n), maybe O(1)* O(1) Pop (Back) O(1) O(1) O(n) O(1) Insert before (given iterator) O(n) O(n) O(n) O(1) Delete (given iterator) O(n) O(n) O(n) O(1) Insert after (given iterator) O(n) O(n) O(1) O(1) Delete after (given iterator) O(n) O(n) O(1) O(1) Get nth element (random access) O(1) O(1) O(n) O(n) Good for implementing stacks yes (back is top) yes yes (front is top) yes Good for implementing queues no yes maybe* yes C++ STL `std::vector` `std::deque` - `std::list` Java Collections `java.util.ArrayList` `java.util.ArrayDeque` - `java.util.LinkedList`
```* singly-linked lists can push to the back in O(1) with the modification that you keep a pointer to the last node
```

Associative containers (sets, associative arrays):

 Sorted Array Sorted Linked List Self-balancing Binary Search Tree Hash Table Find key O(log n) O(n) O(log n) O(1) average O(n) worst Insert element O(n) O(n) O(log n) O(1) average O(n) worst Erase key O(n) O(n) O(log n) O(1) average O(n) worst Erase element (given iterator) O(n) O(1) O(1) O(1) Can traverse in sorted order? yes yes yes no Needs comparison function comparison function comparison function hash function C++ STL - - `std::set``std::map``std::multiset``std::multimap` `__gnu_cxx::hash_set``__gnu_cxx::hash_map``__gnu_cxx::hash_multiset``__gnu_cxx::hash_multimap` Java Collections - - `java.util.TreeSet``java.util.TreeMap` `java.util.HashSet``java.util.HashMap`

Various Types of Trees

 Binary Search AVL Tree Binary Heap (min) Binomial Queue (min) Insert element O(log n) O(log n) O(log n) O(1) (on average) Erase element O(log n) O(log n) unavailable unavailable Delete min element O(log n) O(log n) O(log n) O(log n) Find min element O(log n) O(log n) O(1) O(log n) (can be O(1) if ptr to smallest) Increase key unavailable unavailable O(log n) O(log n) Decrease key unavailable unavailable O(log n) O(log n) Find O(log n) O(log n) unavailable unavailable Delete element O(log n) O(log n) unavailable unavailable Create O(1) O(1) O(1) O(1) find kth smallest O(log n) O(log n) O((k-1)*log n) O(k*log n)

``` [TODO:]
Can also add a table that specifies the best structure for some specific need
e.g. For queues, double linked. For stacks, single linked. For sets, hash tables. etc...
```
``` [TODO:]
Could also contain table with space complexity information (there is a significative cost
in using hashtables or lists implemented via arrays, for example).
```